2025/05/04 by Pylyavskyy, P., Skopenkov, M. · 1 citation
#05E14 #12E20 #14N20 #51A20 #51M15 #57Q05 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2505.02229
The master theorem, introduced independently by Richter-Gebert and by Fomin and the first author, provides a method for proving incidence theorems of projective geometry using triangular tilings of surfaces. We investigate which incidence theorems over C and R can or cannot be proved via the master theorem. For this, we formalize the notion of a tiling proof. We introduce a hierarchy of classes of theorems based on the underlying topological spaces. A key tool is considering the same theorems over finite fields.